Video: Calculating the Initial Volume of a Gas Given the Final Volume and Initial and Final Pressures, Assuming Temperature Is Constant

What volume of gas initially at 2280 torr could be compressed into a 500 L box at 6 atm, assuming the temperature is constant? [A] 20 L [B] 200 L [C] 1000 L [D] 10000 L [E] 100000 L

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Video Transcript

What volume of gas initially at 2280 torr could be compressed into a 500-liter box at six atmospheres, assuming the temperature is constant? A) 20 liters, B) 200 liters, C) 1000 liters, D) 10000 liters, or E) 100000 liters.

In this question, the pressure of a container of gas is being changed from 2280 torr to six atmospheres. The volume of the gas after the pressure has been changed is 500 liters. And we’re being asked to solve for the initial volume of the gas before the pressure was changed.

The question says that the gas was compressed. So it’s most likely that the initial volume will be greater than the final volume, although we’ll see what happens when we solve this problem. The question tells us that the temperature is being held constant. So we can use Boyle’s law to solve this problem.

Boyle’s law tells us that, at a constant temperature, the pressure and volume of a gas are inversely proportional. We can create an expression to solve for the initial volume of the gas by dividing both sides of this expression of Boyle’s law by the initial pressure. Before we plug everything in, you should notice that the initial pressure is in units of torr. But the final pressure is in units of atmosphere. We need both of these units to be the same so that they’ll cancel.

One atmosphere is equal to 760 torr. We can choose to convert either the initial pressure into atmospheres or the final pressure into torr. I’m going to choose to convert the initial pressure from torr into atmospheres. This math is a little tricky to do mentally. But we can simplify it by dividing both numbers by 10. Now we’re left with 228 divided by 76. 76 goes into 228 three times. So our initial pressure is three atmospheres.

Now we can plug all of our values in. The initial pressure we just solved for is three atmospheres. The final pressure was six atmospheres. And the final volume is 500 liters. The atmospheres here cancel, leaving us units of liters, which is the correct units that we’re looking for. To make the math simple, we can take care of the six and the three first. Three goes into six two times. So that leaves us with two times 500 liters, which means the initial volume of the gas was 1000 liters. This matches answer choice C.

This makes sense because, according to Boyle’s law, pressure and volume are inversely proportional. So if the pressure of a gas increases, which it did here. It increased from three atmospheres to six atmospheres. The volume of the gas should decrease, which is what happened. It decreased from 1000 liters to 500 liters.

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